On the Distributed Compression of Quantum Information

The problem of distributed compression for correlated quantum sources is considered. The classical version of this problem was solved by Slepian and Wolf, who showed that distributed compression could take full advantage of redundancy in the local sources created by the presence of correlations. Here it is shown that, in general, this is not the case for quantum sources, by proving a lower bound on the rate sum for irreducible sources of product states which is stronger than the one given by a naive application of Slepian–Wolf. Nonetheless, strategies taking advantage of correlation do exist for some special classes of quantum sources. For example, Devetak and Winter demonstrated the existence of such a strategy when one of the sources is classical. Optimal nontrivial strategies for a different extreme, sources of Bell states, are presented here. In addition, it is explained how distributed compression is connected to other problems in quantum information theory, including information-disturbance questions, entanglement distillation and quantum error correction

Graph Sketches: Sparsification, Spanners, and Subgraphs

When processing massive data sets, a core task is to construct synopses of the data. To be useful, a synopsis data structure should be easy to construct while also yielding good approximations of the relevant properties of the data set. A particularly useful class of synopses are sketches, i.e., those based on linear projections of the data. These are applicable in many models including various parallel, stream, and compressed sensing settings. A rich body of analytic and empirical work exists for sketching numerical data such as the frequencies of a set of entities. Our work investigates graph sketching where the graphs of interest encode the relationships between these entities. The main challenge is to capture this richer structure and build the necessary synopses with only linear measurements. In this paper we consider properties of graphs including the size of the cuts, the distances between nodes, and the prevalence of dense sub-graphs. Our main result is a sketch-based sparsifier construction: we show that O̅(nε-2) random linear projections of a graph on n nodes suffice to (1 + ε) approximate all cut values. Similarly, we show that O(ε-2) linear projections suffice for (additively) approximating the fraction of induced sub-graphs that match a given pattern such as a small clique. Finally, for distance estimation we present sketch-based spanner constructions. In this last result the sketches are adaptive, i.e., the linear projections are performed in a small number of batches where each projection may be chosen dependent on the outcome of earlier sketches. All of the above results immediately give rise to data stream algorithms that also apply to dynamic graph streams where edges are both inserted and deleted. The non-adaptive sketches, such as those for sparsification and subgraphs, give us single-pass algorithms for distributed data streams with insertion and deletions. The adaptive sketches can be used to analyze MapReduce algorithms that use a small number of rounds

Downregulation of FGF Signaling by Spry4 Overexpression Leads to Shape Impairment, Enamel Irregularities, and Delayed Signaling Center Formation in the Mouse Molar.

FGF signaling plays a critical role in tooth development, and mutations in modulators of this pathway produce a number of striking phenotypes. However, many aspects of the role of the FGF pathway in regulating the morphological features and the mineral quality of the dentition remain unknown. Here, we used transgenic mice overexpressing the FGF negative feedback regulator Sprouty4 under the epithelial keratin 14 promoter (K14-Spry4) to achieve downregulation of signaling in the epithelium. This led to highly penetrant defects affecting both cusp morphology and the enamel layer. We characterized the phenotype of erupted molars, identified a developmental delay in K14-Spry4 transgenic embryos, and linked this with changes in the tooth developmental sequence. These data further delineate the role of FGF signaling in the development of the dentition and implicate the pathway in the regulation of tooth mineralization. © 2019 The Authors. JBMR Plus is published by Wiley Periodicals, Inc. on behalf of American Society for Bone and Mineral Research

Harmonic phase-dispersion microscope with a Mach-Zehnder interferometer

Harmonic phase-dispersion microscopy (PDM) is a new imaging technique in which contrast is provided by differences in refractive index at two harmonically related wavelengths. We report a new configuration of the harmonic phase-dispersion microscope in a Mach-Zehnder geometry as an instrument for imaging biological samples. Several improvements on the earlier design are demonstrated, including a single-pass configuration and acousto-optic modulators for generating the heterodyne signals without mechanical arm scanning. We demonstrate quantitative phase-dispersion images of test structures and biological samples

Essays in Financial Engineering

This thesis consists of three essays in financial engineering. In particular we study problems in option pricing, stochastic control and risk management. In the first essay, we develop an accurate and efficient pricing approach for options on leveraged ETFs (LETFs). Our approach allows us to price these options quickly and in a manner that is consistent with the underlying ETF price dynamics. The numerical results also demonstrate that LETF option prices have model-dependency particularly in high-volatility environments. In the second essay, we extend a linear programming (LP) technique for approximately solving high-dimensional control problems in a diffusion setting. The original LP technique applies to finite horizon problems with an exponentially-distributed horizon, T. We extend the approach to fixed horizon problems. We then apply these techniques to dynamic portfolio optimization problems and evaluate their performance using convex duality methods. The numerical results suggest that the LP approach is a very promising one for tackling high-dimensional control problems. In the final essay, we propose a factor model-based approach for performing scenario analysis in a risk management context. We argue that our approach addresses some important drawbacks to a standard scenario analysis and, in a preliminary numerical investigation with option portfolios, we show that it produces superior results as well

Exploring the Morphology of High-Resolution 3D Printed Scaffolds for Tissue Engineering

Three-dimensional (3D) printing or additive manufacturing (AM) is a technique that is commonly used within tissue engineering and regenerative medicine (TERM). Among AM techniques, melt electrowriting (MEW) is known for its high-resolution capabilities, which utilizes thermoplastic materials to produce scaffolds with microscale structures for tissue engineering (TE). Although more popular in recent years, MEW is still underdeveloped, causing the majority of MEW scaffolds utilized within TE to have a 0°/90° laydown pattern. This study explores different laydown pattern (0°/90°, 0°/60°/120°, and 0°/36°/72°/108°/144°) scaffolds made of poly(ε-caprolactone) (PCL) and how these scaffolds are morphologically different and affect cell seeding. The results show that cell seeding was similar between all of the different laydown patterns, with a more even distribution found in the 0°/36°/72°/108°/144°) scaffold due to the better 3D interconnectivity found in this design